A light emitting device is widely used as a display or lighting. In recent years, the higher output of the light emitting device has been expected in terms of an improvement in the performance of the display or the like. To provide the higher output, an improvement in the light extraction efficiency of the light emitting device is required. In order to improve the light extraction efficiency, there is proposed, e.g., a method for forming roughness on the surface of the light emitting device instead of forming a planarized surface. With regard to the size of the roughness, it is known that the effect of a structure of a wavelength order is high, and the extraction efficiency is improved especially in a photonic crystal structure where a refractivity index is periodically changed by the roughness of the wavelength order (U.S. Pat. Specification No. 3,739,217, U.S. Pat. Specification No. 5,955,749). As a crystal structure where a two-dimensional photonic band gap is concurrently formed either in a TE mode or a TM mode, there is known a crystal structure of a circular-hole arrangement type. Conventionally, there has been known a method for forming the roughness using photolithography. However, it has been difficult to form fine roughness in the size of a visible light wavelength in accordance with this method. Consequently, X-ray exposure or electron beam exposure has been examined for the formation of the fine roughness. However, it is not practical to adopt the X-ray exposure or the electron beam exposure since a large size X-ray source facility is required in the X-ray exposure, and the electron beam exposure requires a very long period of time. Accordingly, as another method, there is proposed the formation of the fine roughness by performing etching using a nano-sized particle as a mask (U.S. Pat. Specification No. 4,407,695).
However, the size of the roughness depends on the size of the nano-sized particle in this method. To change the size of the roughness, the nano-sized particle needs to be changed, and therefore fine adjustment of the size of the roughness has been difficult. The configuration of the roughness to be formed is limited to a configuration where holes are formed in the gap between particles or a configuration where the portion immediately below a particle portion is left in a shape of a conical trapezoid. Therefore, the structure with a column arrangement type can be formed. However, the formation of the structure of the circular-hole arrangement type has been difficult.